I have no idea what some of you are talking about sometimes. I've always felt like I had no laning presence with Annie.
Here's a list of champions I can think of that can always win a solo lane against Annie.
Anivia
Ashe
Brand
Caitlyn
Ezreal
Fiddlesticks
Gangplank
Heimerdinger
Miss Fortune
Vayne
Vladimir
These are the ones you just plain can't do anything about. With most other champions, your odds are more fair, but it's never even remotely easy.
You will always lose a 2v1 as Annie. Any two champions in the game can kill you while you're at full health. You can stop this from happening by not walking past your lane's halfway point. But if your opponents have some form of CC, then you're not safe even that far out. You have to play the entire lane inside flash range of your turret.
Same thing applies to 2v2. There have been plenty of times where my two opponents have ignored my ally completely to run in and kill me from full health. If you're ally can't get people off of you, it's the same situation as a 2v1.
The only saving grace I have is that most people don't realize how fast they can make Annie's health drop by playing aggressively. Or they're intimidated by a laning partner they don't really need to worry about.
Sure, you can disintigrate them for gobs off their health, but it doesn't matter when they can immediately kill you afterward. I'm not saying Annie is a terrible laner, but some of you people make it sound like she's god mode.
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"What if you just eat vegetarians?"-neonreaper
"^ You are what you eat. ^_~"-Koiji